Question

How do I solve this? Can you show me step by step process.

Answer 1

(Q14) To find the equation when given the gradient and one set of points (or coordinates), you have to solve for b. 
1. Identify the gradient and x- and y- intercepts. 
    m=3, x=1, y=5
2. Substitute them into the equation, y=mx+b. 
    5=3(1) + b 
3. Solve for b.
    5=3 + b 
    b=2 
4. Rewrite the equation. 
   y=3x+ 2
(Q15) To find the equation when given two sets of points, you need to.
1. Find the gradient, using the formula, (x2-x1 / y2-y1) 
   (7,5) and (4, -7)
    x1=7, x2= 4, y1=5, y2=-7
    4-7/-7-5 = -3/-12 = 1/4 
   Therefore, gradient = 1/4 
2. Substitute with one set of points (can be either (7,5) or (4,-7) in this example - question 15) into the equation, (like you did in question 14) 
  a) Identify the gradient and x- and y- intercepts. 
   m=1/4, x=7, y=5
  b) Solve for b. 
   5=1/4(7) + b
   5=7/4 + b 
   b=13/4 or 3 1/4 
  c) Rewrite the equation.
   y=1/4x + 13/4